if m= tan Theta + sin theta n=tan theta - sin theta prove that (m²-n²)²=16mn
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Answered by
7
Answer:
tan + sin = m tan - sin = n (m + n) (m - n) = 2 tan 2 sin m2 - n2 = 4 tan sin L.H.S. = (m2 - n2)2= 16 tan2sin2 R.H.S. = 16 mn = 16 (tan + sin ) (tan - sin ) = 16 (tan2- sin2) = 16 = 16 = 16 = 16 tan2sin2 L.H.S. = R.H.S.
Answered by
7
Answer:
(tan θ + sin θ) = m and (tan θ − sin θ) = n
To Prove: (m2 − n2)2 = 16mn
L.H.S. = (m2 − n2)2
= [(tan θ + sin θ)2 – (tan θ − sin θ)2]2
= (4tan θ sin θ)2
= 16 tan2 θ sin2 θ …(1)
R.H.S. = 16mn
= 16(tan θ + sin θ)(tan θ − sin θ)
= 16(tan2 θ − sin2 θ)
= 16 [{sin2 θ (1-cos2 θ)/cos2θ]
= 16 x sin2 θ/cos2θ x (1-cos2 θ)
= 16 tan2 θ sin2 θ …(2)
From (1) and (2)
L.H.S. = R.H.S.
Step-by-step explanation:
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